Detailed kinetic investigation of the C2H5 + Cl2 reaction and analysis of the reaction of CH3 + Cl2 initiated by H-atom contamination at 298 K and at millitorr pressures

Article abstract of DOI:10.1524/zpch.2001.215.3.283

The bimolecular reaction: C₂H₅+Cl₂ →4 C₂H₅Cl+Cl is studied in the very low pressure reactor (VLPR) system at 298 K starting with Cl/C₂H₆/Cl₂ mixtures. Mass conservation is found to be 97±3% for the overall chemical change in the system. From the C₂H₅Cl product formation kinetics, k₄ = (1.05±0.05) · 10^-12 cm³/(molecule-s) is derived. Two independent estimates of the A factor gives A₄ = 1.3 · 10^-12 cm³/(molecule-s). These parameters yield a positive activation energy of 0.13 kcal/mol in contrast with recently reported negative activation energy values. Some side reactions of small extent are initiated by H atom contamination in the system. The measurement of CH₃Cl product formed from CH₃+Cl₂ →11 CH₃Cl+Cl gives k₁₁ = (3.4±0.3) · 10^-12 cm³/(molecule-s) with an estimated A factor of A₁₁ = 5.0 · 10^-12 cm³/(molecules). The source of CH₃ radicals is the side reaction H+C₂H₅ → 2CH₃. by Oldenbourg Wissenschaftsverlag, Muenchen.

Full text of DOI:10.1524/zpch.2001.215.3.283

Zeitschrift für Physikalische Chemie, 215, 3, 283–304 (2001)
by Oldenbourg Wissenschaftsverlag, München

Detailed Kinetic Investigation of the
C H + Cl Reaction and Analysis of the
2
5
2
Reaction of CH + Cl Initiated by H-Atom
3
2
Contamination at 298 K and at Millitorr
Pressures
∗
By Otto Dobis and Sidney W. Benson
Loker Hydrocarbon Research Institute, University of Southern California,
University Park, Los Angeles, California 90089-1661, USA
Dedicated to Prof. Dr. Dr. h.c. mult. Jürgen Troe
on the occasion of his 60th birthday
(Received June 6, 2000; accepted August 11, 2000)
Kinetics / Cl / Ethyl / Methyl / Radical Reactions
2
4
The bimolecular reaction: C
2
H
5
+Cl
2
−→ C
2
H
5
Cl+Cl is studied in the very low pressure
/Cl mixtures. Mass conservation
is found to be 97± 3% for the overall chemical change in the system. From the
reactor (VLPR) system at 298 K starting with Cl/C
2
H
6
2
−12
3
C
2
H
5
Cl product formation kinetics, k
4
= (1.05± 0.05)·10 cm /(molecule-s) is derived.
−
4
12
3
Two independent estimates of the A factor gives A
= 1.3·10 cm /(molecule-s). These
parameters yield a positive activation energy of 0.13 kcal/mol in contrast with recently
reported negative activation energy values. Some side reactions of small extent are
initiated by H atom contamination in the system. The measurement of CH
3
Cl product
11
−12
3
formed from CH
3
+Cl
2
−→ CH
3
Cl +Cl gives k11 = (3.4± 0.3)·10 cm /(molecule-s)
−12
3
with an estimated A factor of A11 = 5.0·10 cm /(molecules). The source of CH
3
radicals is the side reaction H+C
2
H
5
→ 2CH
3
.
Introduction
The free radical reaction between halogens and simple alkanes have provided
classical examples of chain reactions. Initial studies gave overall rate constants
which were combinations of the individual rate constants for initiation, propa-
gation and termination steps [1–3]. The last 40 years have witnessed extensive
*
Corresponding author. E-mail: benson@bfc.usc.edu

2
84
O. Dobis and S. W. Benson
studies of individual step reactions [4, 5]. While most of these have explored
halogen atom-alkane reactions
a
X+RH ←→ HX+R
relatively few have studied the equally important second chain step of halogen
molecules with alkyl radicals:
b
R+X ←→ RX+X .
2
The reaction of ethyl radical with chlorine, an important prototype of
reaction b has been studied by a number of groups whose reported rate con-
stants cover a range [6–8] of a factor of 5.5. The frequently quoted result
−
12
3
k = 3.9·10 cm /(molecule-s) by Goldfinger et al. [9] is not a measurement
4
but only a preliminary estimate. It was never measured directly due to problems
with O contamination of the reagents [10].
2
Relative rate measurements in the photo-chlorination study of the
Cl /C H /O stationary system with high excess of Cl and O concentra-
2
2
6
2
2
2
tions have provided rate constant ratios k /k , where k is the rate constant
4
ref
ref
for the competing radical inhibition step C H +O . Based on gas chromato-
2
5
2
graphy determination of products [11], k /k = 1.75 was found, while studies
4
ref
based on using the IR spectra of C H consumption and C H Cl formation [12]
2
6
2
5
gave k /k = 1.99, both measured at 650–700 Torr total pressures. Convert-
4
ref
ing these ratios into an absolute value for k is hindered by the range of high
4
pressure limit values for k . These range from low values [13, 14] of (4.4−
ref
−12
−12
3
5
.3)·10 to highs [15] of (7.8−9.2)·10 cm /(molecule-s). Besides some
questionable simplifications made in that chemically very complex system,
the uncertainty of kref alone introduces a factor of two uncertainty in k . Ki-
4
netic measurements in the same competitive photo-chlorination system using
a more detailed mechanism, which included the UV absorption intensity de-
pendence on the O /Cl ratio, reported [9] k /k = 3.58 at 400 Torr overall
2
2
4
ref
pressure.
In our recent paper [16] we have noted some inconsistencies in the rate pa-
rameters of reaction b which are especially striking when compared with those
for the CH +Cl reaction. This and the above lack of consensus in the rate
3
2
constant value of the C H +Cl reaction makes appropriate a further experi-
2
5
2
mental investigation using alternative methods. Our very low pressure reactor
VLPR) system is well suited to do this.
(
Experimental section
The VLPR system used for current measurements is the same three-stage, all
turbo-pumped equipment used for previous kinetic studies [17]. Although it

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
285
has been described earlier [18], the system parameters, experimental sequence,
MS analysis, and data treatment are briefly summarized here.
The basic part of the system is the thin-teflon-coated, cylindrical, ther-
3
mostated, Knudsen flow cell reactor of volume V = 217.5 cm mounted on
r
the top of the main vacuum chamber. Three separate gas inlets are affixed on
the top of this reactor, each preceded by a resistive capillary flow subsystem
calibrated for regulating the fluxes of initial gas components with the use of
Validyne transducers. One of the inlets is connected through a H PO coated
3
4
quartz discharge tube centered in the Opthos microwave generator cavity of
a McCarrol antenna and joined at the tapered capillary inlet of the reactor cell.
This inlet is used to introduce a 5% Cl /He gas mixture. It provides the ini-
2
tial Cl atom concentration in the reactor upon running the microwave generator.
The second inlet is used for a 7.5% C H /He gas mixture flow and the third
2
6
one supplies a 10% Cl /He flow. They provide the initial C H and Cl reactant
2
2
6
2
concentrations, respectively.
The reactor base is sealed to a teflon-coated, rapidly adjustable slide mech-
anism having three interchangeable escape orifices [18] with diameters of
st
0
.193, 0.277, and 0.485 cm. They permit changing the 1 order escape rate
constants of gases, k , which allows variation of the reactor residence time
eM
by a factor of 5. The use of these orifice sizes in different experimental runs
is indicated as φ , φ , and φ , respectively, in Tables 1 and 2, and are marked
2
3
5
with different data symbols in Figs. 3–6. With our reactor volume V , the first-
r
order escape rate constant for any gas component of mass M is given by the
1
/2 −1
Knudsen equation keM = a (T/M) s , where T is the absolute temperature
φ
and a = 0.258 for φ , 0.546 for φ , and 1.321 for φ orifices [18]. All escape
φ
2
3
5
rate constants appearing in Eqs. (1–11) were calculated with the above formula.
The well controlled gas inlet and outlet dynamics establishes the strictly de-
fined steady state flow condition in the reactor which operates in the Knudsen
flow regime.
Mass spectral calibration for a given gas component of mass M is carried
out by measuring the mass signal intensity I as a function of the specific flux
M
F(M) according to the relationship I = α F(M), where α is the mass spec-
M
M
M
3
tral efficiency for mass M and F(M) = flux/V in units of molecules/(cm -s).
r
This relationship is strictly linear in the mass flow range used as is shown in
Fig. 2. The steady-state concentration of the gas component M in the reactor
cell can then be calculated from the relation [M] = F(M)/k .
eM
The gas mixture of products and unreacted reagents leaves the reac-
tor in the form of an effusive molecular beam. This beam is chopped by
a tuning fork and collimated by two successive pinholes in the differen-
tially pumped vacuum system to reduce the background signal. The beam
is sampled with the off-axis mass analyzer of a quadrupole mass spectrom-
eter and the mass signals are fed to a phase sensitive lock-in amplifier tuned
to the chopping frequency. This chopping and phase sensitive detection en-
sures that we are sampling species which have not made collisions after leav-

2
86
O. Dobis and S. W. Benson
ing the reactor. The measured mass ranges are repeatedly scanned, usually
0–30 times, to give a good statistical average and the mass intensities are
2
recorded for data acquisition. Each mass signal is corrected for any small back-
ground value recorded both prior to start-up of mass flow and following a run
sequence.
In a typical operation, the Cl flow is started first through the microwave
2
discharge inlet and the mass signal of Cl isotopes (at 70, 72 and 74 AMU) are
2
repeatedly recorded. This measurement serves for the check of the mass spec-
tral sensitivity using the known Cl flow as standard. The microwave generator
2
is then turned on and its power is adjusted to total dissociation of Cl observed
2
by the disappearance of Cl mass signals and their replacement by Cl atom
2
and HCl signals. After the Cl/HCl signal ratio has reached a steady value, the
mass range (M/z) of 35–38 is repeatedly scanned using 20 V electron energy
and the Cl/HCl signal distribution is calculated (column 2 of Table 1). The ini-
tial steady state Cl concentration is calculated using a Cl atom mass balance as
[
Cl] = 2F(Cl )I /(I + I )k , where F(Cl ) is the specific flow rate of Cl
0
2
Cl
Cl
HCl
eM
2
2
3
(
molecules/cm −s). These values are given in column 3 of Table 1. Note that
the mass signals I are proportional to the flux of species m. For Cl atom and
m
HCl the sensitivities are found to be the same [17].
Next, the C H flow is started through the second inlet and gradually in-
2
6
creased until a sizable decrease of Cl signal (accompanied by an increase in
HCl signal) is observed. The initial C H concentration (column 4 of Table 1) is
2
6
calculated from the inlet flow rate F(C H ) . The new Cl and HCl signal inten-
2
6 0
sities are repeatedly scanned using 20 eV and the Cl/HCl distribution as well
as the Cl concentration (columns 5 and 6 of Table 1, respectively) are calcu-
lated as before. Then the mass spectrometer is set to scan the mass range 25–30
using both 20 V and 40 V electron energies. The C H concentration (column 7
2
6
of Table 1) is then calculated from the average mass 30 intensities measured
at both voltages. The mass spectral calibration of ethane has been described
earlier [17, 19].
Finally, the flow of Cl is started thorough the third inlet and increased
2
gradually until the product C H Cl appears (mass range 60–66) with measur-
2
5
able signal intensities at masses 64 and 66. The mass range 35–38 is scanned
again using 20 V electron energy for the measurement of changes in the Cl
and HCl intensities, then mass ranges of 25–30, 49–52, 60–66, and 70–74 are
scanned using both 20 V and 40 V electron energies.
Treatment of data
The begining of each run repeats the kinetic investigation of the Cl/C H
2
6
system which provides the initial steady state ethyl radical concentration ac-
cording to the well explored mechanism [17]:

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
287
1
Cl +C H −→ HCl +C H
2
6
2
5
4
2
Cl +C H −→ HCl +C H
2
5
2
3
2
C H −→ C H +C H .
2
5
2
6
2
4
At low [C H ] /[Cl] ratios (≤ 0.2), reactions
2
6
0
0
−
→
Cl +C H
HCl +C H
2
4
←−
2
3
2
Cl +C H −→ HCl +C H
2
3
2

2
88
O. Dobis and S. W. Benson
also contribute to the mechanism, but that condition is outside the scope of the
present experimental runs (Table 1).
From the steady state kinetics for ethane [RH] and ethyl radical [R] concen-
trations the ethyl radical concentration [R] can be derived [17] as
2
∆[RH]k −k [RH][Cl]
eRH
1
[
R] ≈
,
(1)
k [Cl]+k
2
eR
where ∆[RH] = [C H ] − [C H ]. Using the known rate constant values
2
6
0
2
6
−11
−11
3
of k = 6.1·10
and k = 1.20·10 cm /(molecule-s) at room tempera-
1
2
ture [17], the calculated ethyl radical concentrations are given in column 8
of Table 1. In turn, the corresponding F(C H ) values of these ethyl radical
2
5
concentrations are proportional to the increase of I29 signal intensities over
the fragment signal contribution from I30 of ethane. This excess can be cal-
culated as ∆I = I − I α /α , where α is the mass spectral efficiency
29
29
30 29
RH
RH
of RH at mass 30 and α29 is the partial mass spectral sensitivity contribu-
tion of RH fragmentation [17, 19] to mass 29 in the RH range of mass 25–30.
The mass spectral efficiency of the ethyl radical (α ) then can be calculated
R
from these data as α = ∆I /[R]k . α values averaged for all experimental
R
29
eR
R
−11
runs of Table 1 are obtained as α (V = 20 eV) = (0.788± 0.066)·10
and
R
−
11
α (V = 40 eV) = (1.321± 0.050)·10 . They are in good agreement with α
R
R
values measured in our earlier work [17, 19].
When Cl is introduced into the system as the third inlet component using
2
different flow rates which correspond to initial [Cl ] concentrations given in
2
0
column 2 of Table 2, the entire mass spectrum range recorded from mass 25
up to mass 74 shows significant changes, a response to new chemical reac-
tions. The decreased Cl concentration (column 5 of Table 2) can be calculated
2
from the average of mass 70 signal intensities measured using both 20 eV and
4
0 eV energies. The mass 35 signal was used to measure the Cl concentration
+
directly, but now has to be corrected for the Cl contribution from Cl frag-
2
mentation [20] which is 0.67% of Cl with 20 eV spectrometry. Since the HCl
2
+
concentration is relatively high in each run, a second correction of 0.24% Cl
contribution [17] of HCl fragmentation is also used. After these corrections,
the calculated Cl atom concentrations for each run are given in column 3 of
Table 2. Since chlorinated hydrocarbon products are now formed in the system,
the Cl/HCl distribution cannot be derived from the Cl consumption balance.
2
Therefore, the HCl concentrations, given in column 4 of Table 2, are calcu-
lated from the measured mass 36 signal intensities [17] using the measured
α = αHCl.
Cl
Ethane concentrations, given in column 6 of Table 2, are calculated from
the mass 30 signal intensities measured with both 20 eV and 40 eV spectrom-
etry. This signal does not interfere with any fragment signal from chlorinated
products. But mass 29 the signal of C H radical has an extra fragment contri-
2
5
bution from the C H Cl product [21]. The direct relationship between I and
2
5
29
I66 is shown in Fig. 1, where the plotted data are taken from the overall mass

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
289
analysis of C H Cl in the mass range from mass 25 to mass 66. The slopes in
2
5
Fig. 1 are 0.620± 0.022 for 40 eV and 0.540± 0.023 for 20 eV spectrometry.
After making these corrections, the ethyl radical concentrations, given in col-
umn 7 of Table 2, are calculated from the ∆I29 intensities using the known αR

2
90
O. Dobis and S. W. Benson
Fig. 1. Direct relationship between the intensities (in arbitrary units) of mass 29 and the
3
7
parent mass 66 of ethyl chloride ( Cl isotope) used for the correction of the ethyl radical
spectrum at 20 V and 40 V ionization energies.
and keR values. Ethyl chloride concentrations, given in column 8 of Table 2, are
calculated from the measured I66 mass signal values, which are the fragment
37
interference free signals [21] of the Cl isotope of C H Cl.
2
5
Mass scanning showed some unexpected new signals at masses of 50 and
52 which were identified as the signals of methyl chloride. Our mass spec-
trometer is very sensitive to CH Cl, so that even a small amount of CH Cl
3
3
can be measured accurately. Fig. 2 shows the mass spectral calibration of
CH Cl where the slopes correspond to the total mass spectral efficiencies:
3
ꢀ
−10
−11
α = (2.404± 0.028)·10 with 40 V and (7.665± 0.182)·10 with 20 V
ionization energies in the measured mass range. The mass intensity distribu-
tions (in percentage) at the two electron voltages are for 40 eV:
I : I : I : I : I = 2.50 : 1.44 : 4.79 : 67.87 : 1.48 : 21.92
47
49
50
51
52
from which the cross-section efficiency for mass 50 can be easily obtained
ꢀ
−10
as α = 0.6787·α (V = 40 V) = 1.632·10 and similarly for mass 52. For
5
0
2
0 eV:
I : I : I : I : I = 0.37 : 3.94 : 70.47 : 2.22 : 22.99
47
49
50
51
52

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
291
Fig. 2. Sum of signal intensities of methyl chloride recorded from mass 47 to mass 52 at
various specific flow rates of 5.00% CH Cl/He mixture using 20 V and 40 V ionization
3
energies.
and αCH3Cl values for each isotope mass are calculated in the same way as for
40 eV spectrometry.
With the above quantitative calibration, the CH Cl concentration is calcu-
3
lated for each run from the I50 and I52 signal intensities measured with both
0 eV and 40 eV electron energies. Its concentrations are given in column 9 of
Table 2.
Vinyl chloride product concentrations, given in column 11 of Table 2, are
calculated from the measured I signal intensities after correcting them for the
2
62
C H Cl fragment contributions. The C H Cl mass spectrometry and the reso-
2
5
2
3
lution of its I signal in a C H Cl/C H Cl composition were presented in our
62
2
3
2
5
previous work [21].
Chloroethyl radical concentrations can be obtained in principle from the
excess signal intensities [21] of mass 65. However, since the corrected ∆I65
values are small in all experimental runs and the α
value is also low [21],
R•Cl
this method is inaccurate for low C H Cl concentration measurements. More
2
4
accurate results can be obtained by calculating the chloroethyl radical con-
centration from its steady state formation and consumption kinetics (Eqs. 7
ꢀ
and 7 ) using known rate constant values. These calculated C H Cl concentra-
2
4
tion values are listed in column 12 of Table 2.

2
92
O. Dobis and S. W. Benson
Ethylene concentration, given in column 10 of Table 2, are calculated
from the measured I28 signal intensities after multiple corrections for contri-
butions from other mass 28 sources. These corrections arise from the con-
tributions of C H and C H radical fragmentations [19], as well as of the
2
6
2
5
C H Cl fragment [21] of I . Each correction contributes considerably. Al-
2
5
28
together they reduce the originally measured I28 signal by about 60%–90%
with 40 eV and 50%–80% with 20 eV spectrometry. Consequently, the meas-
ured ∆I28 has much more scatter than the other mass intensity corrections
which usually amount to only a few percent. The calculated ∆I28 values are
then converted into C H concentrations using the known α cross-section
2
4
C2H4
efficiency [17].
Results
Mass analysis indicates that a much more complex reaction mechanism occurs
in the system when Cl reactant is introduced as the third reaction component
2
than we had anticipated. Before going into the kinetic details of this extended
reaction mechanism it is instructive to examine the mass balances of Cl atom
and ethane. Regardless of the reaction mechanism, the Cl atom conversion can
be summed up and equated to the overall chlorinated product formed in the
system:
∆
[Cl]keCl +2∆[Cl ]k
= −∆[HCl]k
+ F(RCl)+ F(C H Cl),
2
eCl2
eHCl
2
3
+
F(CH Cl)+ F(C H Cl).
(2)
3
2
4
Note that the HCl concentration is increasing with the progress of reac-
tion, therefore, its change is negative according to the convention: ∆[HCl] =
[
HCl] −[HCl]. F(C H Cl) is a very small term in Eq. (2), its usually does not
0
2
4
exceed 1% of the overall chlorine products in most of the experimental runs.
The mass flow data can be calculated from the corresponding concentra-
tions listed in Tables 1 and 2 for each run. They are plotted according to Eq. (2)
in Fig. 3. The slope of this linear relationship indicates that our mass analysis
accounts for 99% of the Cl atom in the system. The last mean squares com-
puted line of Fig. 3 goes through the origin. The bulk of chlorinated product
is HCl. The flow of chlorinated hydrocarbons amount to only 5%–10% when
12
3
[
Cl ] < 1·10 molecule/cm , but may go up to 22% with increased Cl con-
2
2
centrations.
A similar balance can be found for carbon:
•
1
2
∆
[RH]keRH = F(R )+ F(RCl)+ F(CH Cl)
(3)
3
1
2
+
F(C H Cl)+ F(C H )+ F(CH ) .
2
4
2
4
3
Substituting the mass flow data calculated from the concentration values of
Tables 1 and 2 for each run, the results are shown in Fig. 4. The slope indi-
cates that the product recovery is 98%. Within this flow balance, chlorinated

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
293
Fig. 3. Mass flow balance between Cl atom consumption and chlorinated product forma-
tion plotted according to Eq. (2). Symbols of orifices for data pairs are ꢁ, φ , ꢂ, φ
2
3
,
,
5
φ .
hydrocarbon products account for 10%–15% at low Cl concentrations, but
2
they can reach 36% at the highest Cl concentration. The very small intercept,
2
11
3
0
.2·10 molecule/(cm -s), is within the analytical uncertainty of 2%.
The reaction mechanism and the overall kinetics must satisfy the above
mass balances. The product distributions in Table 2 indicates that the mechan-
ism is complex. However, the considerable decrease of C H reactant, as well
2
6
as the increase of HCl product in each run show that the chain is rapid and that
the fastest step in the chain is reaction 1. The ethane consumption and the for-
mation of C products point to the following new reactions in the Cl/C H /Cl
2
2
6
2
three component reaction system:
4
Cl +C H −→ C H Cl +Cl
2
2
5
2
5
5
Cl +C H Cl −→ C H Cl +HCl
2
5
2
4
6
Cl +C H Cl −→ C H Cl +HCl
2
4
2
3
7
Cl +C H Cl −→ C H Cl +Cl
2
2
4
2
4
2

2
94
O. Dobis and S. W. Benson
2
Fig. 4. Mass flow balance between ethane consumption and C product formation plotted
according to Eq. (3). Symbols of orifices are the same as in Fig. 3.
8
2
C H Cl −→ C H Cl +C H Cl
2
4
2
5
2
3
8a
C H Cl+C H −→ C H +C H Cl
2
4
2
5
2
6
2
3
8
b
−→ C H Cl +C H
2
5
2
4
Rate constants of reactions 5–8 are all known. They have been meas-
ured in the Cl/C H Cl two component reaction system in our previous
2
5
−12
−11
study [21]. They are: k = (8.07± 0.06)·10 , k = (1.18± 0.04)·10 , and
5
6
−12
3
k = (1.83± 0.15)·10 cm /(molecule-s). Reaction 7 is slow. Its rate con-
8
−
13
3
stant was measured [21] as k = (1.7± 1.0)·10 cm /(molecule-s). In the
7
present work, only traces of C H Cl product was observed at masses 83 and
2
4
2
9
8 in some runs with very high Cl concentrations. Rate constants for radi-
2
cal disproportionations 8a and 8b are not known, but, since k ∼ k , it seems
8
3
reasonable to expect that they also have about the same value as k .
3
The steady state condition for C H Cl formation leads to the kinetic equa-
2
5
tion:
•
•
k [R][Cl ] = (k [Cl]+k )[RCl]−(k [R Cl]+k [R])[R Cl],
(4)
4
2
5
eRCl
8
8b
•
where R Cl denotes C H Cl radical (two isomers). Since the C H Cl radical
2
4
2
4
concentration is very small in all runs, the last two terms of the right side are

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
295
Fig. 5. Ethyl chloride formation kinetics plotted according to Eq. (6). The slope gives k
directly. Symbols of orifices are the same as in Fig. 3.
4
much smaller than the first two and may be neglected with a maximum error of
0%. Their contribution can be assessed from the steady state kinetics of vinyl
1
chloride (VCl) formation:
•
•
•
keVCl[VCl] = k [R Cl]+(k [R Cl]+k [R])[R Cl].
(5)
6
8
8a
•
2
It can be shown using measured and estimated concentrations that the k [R Cl]
8
•
term is negligible compared to k [R Cl][Cl] while the k term is ∼ 10% of the
6
8a
k term. Neglecting both radical-radical disproportionation rates implies that
6
the bulk of the small vinyl chloride product would be formed in reaction 6,
the rate constant of which is about one order of magnitude higher than that of
reaction 8 or 8a. Thus we can write for Eq. (4):
k [Cl ] ≈ (k [Cl]+keRCl)[RCl]/[R] ,
(6)
4
2
5
with less than 10% error. The plot of data according to equation 6 is pre-
sented in Fig. 5 where the slope gives the rate constant of reaction 4 directly
−12
3
as k = (1.05 ± 0.05)·10 cm /(molecule-s). Due to the approximation in
4

2
96
O. Dobis and S. W. Benson
Eq. (6), k is actually an upper limit, but the average deviation introduced by
4
Eq. (6) does not exceed the 5% scatter.
The inaccuracy of the direct mass spectral measurement of low C H Cl
2
4
radical concentrations can be bypassed by solving the steady state kinetic
equation for the chloroethyl radical concentration. With the use of the above
approximation for k and k , it leads to:
8a
8b
k [RCl][Cl]
•
5
[
R Cl] ≈
.
(7)
k [Cl]+k [Cl ]+k
•
6
7
2
eR Cl
Also from Eq. (5) we can derive an alternate approximation:
keVCl[VCl]
•
ꢀ
[
R Cl] ≈
.
(7 )
k [Cl]+k [R]
6
8a
The C H Cl concentrations given in column 12 of Table 2 were calculated ac-
2
4
ꢀ
cording to the average of Eqs. (7) and (7 ) using known rate constants and
measured concentration values given in Table 2.
It has been shown earlier that our H PO coated microwave discharge tube
3
4
produces a low H atom concentration in the reactor cell [20]. In the present
three component starting system they react with Cl , (causing increased Cl
2
2
consumption) and also with ethyl radical. This latter reaction leads to cracking
of the C−C bond and to CH radical formation. CH is the precursor of CH Cl
3
3
3
which is a measured side product. It hampers the otherwise direct calculation
of k from the Cl consumption kinetics, but allows us to explore the kinetics
4
2
of some of the side reactions initiated by the H atom.
These new reactions are:
9
H+Cl −→ HCl +Cl
2
10
H+C H −→ 2CH
2
5
3
10a
−
→ H +C H
2
2
4
1
1
Cl +CH −→ CH Cl +Cl
2
3
3
12
CH +C H −→ CH +C H
3
2
5
4
2
4
12a
CH +C H Cl −→ CH +C H Cl
3
2
4
4
2
3
13
Cl +CH Cl −→ HCl +CH Cl
3
2
14
CH +HCl −→ CH +Cl
3
4
15
H+HCl −→ H +Cl.
2
k was investigated in the same VLPR system [20]. Its rate constant is
9
−12
3
found to be k = (9.6± 0.4)·10 cm /(molecule-s). Radical disproportion-
9
ation reaction 12 has the same rate constant value [22] as k and we sup-
3

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
297
pose that k12a ≈ k . Reactions 13, 14 and 15 are all slow and have mea-
12
ger contributions to the overall kinetics except in a few cases of high HCl
concentration. Their rate constant values are known with consensus [23, 24].
−13
3
k13 = 5·10 cm /(molecule-s) is reported from both relative [25] and ab-
−
13
13
3
solute [26] rate measurements at 298 K. k = 1·10 cm /(molecule-s) was
14
−
3
measured in our earlier work [19]. k15 = 4.5·10 cm /(molecule-s) is an
average value of reported [27] experimental measurements. These rate con-
stant values can be used for the derivation of a kinetic interrelation between k10
and k .
11
Some other possible side reactions of H atom consumption, such as:
H+C H +M → C H +M
2
5
2
6
rd
is excluded due to the absence of effective 3 body collider at mTorr pressures,
and reactions
H+C H Cl → HCl +C H
2
4
2
4
H+CH Cl → CH +Cl (or CH +HCl)
2
3
2
are neglected because of the low concentrations of reactants.
Due to the low concentration of species involved in reactions 9–15 and the
much larger error in treating them, we shall not deal with their kinetics here.
Some comments will be made about reaction 11 for which even less precise
values are of interest.
A steady state kinetic equation for the measured CH Cl product formation
3
can be written as
k [CH ][Cl ] = (k [Cl]+k
)[CH Cl] .
(8)
11
3
2
13
eMeCl
3
Substituting it into the equation for the consumption of Cl by H atoms, C H
5
2
2
and CH radicals, we have
3
•
∆
[Cl ]k −(k [R]+k [R Cl])[Cl ]−(k [Cl]+k
)[CH Cl]
(9)
2
eCl2
4
7
2
13
eMeCl
3
=
k [H][Cl ] .
9
2
On the other hand, the sum of steady state kinetic equations for Cl and Cl2
consumptions as well as for HCl formation gives
∆
[Cl]keCl +∆[Cl ]k +∆[HCl]keHCl = −k [H][Cl ].
(10)
2
eCl2
9
2
With known rate constants [20, 23–25] for k and k , we can calculate the
9
13
steady state values of [H] from both Eqs. (9) and (10). They give the same H
atom concentrations with a 10% deviation at most. Their averages calculated
10
3
for each run are in the range (2−8)·10 atoms/cm , somewhat higher than we
observed earlier [20].

2
98
O. Dobis and S. W. Benson
Fig. 6. Combined flow balance change and chlorinated product formation kinetics plotted
according to Eq. (11). The slope gives k directly. Symbols of orifices are the same as in
4
Fig. 3.
Values of H atom concentrations calculated in this way can now be used to
make a best fit of k and k11 to the known [H]. From this we find k ≈ (3.4±
1
0
11
−
12
3
0
.3)·10 cm /(molecule-s). Substituting it into Eq. (8), the steady state CH
3
radical concentrations can be calculated for each run. Their values are given in
1
2
column 13 of Table 2. Half of its flow rate [CH ]k contributes to the C2-
3
eMe
product formation.
Combination of the kinetic Eq. (9) with the flow balance Eq. (10) leads to
an alternative equation for k4:
ꢁ2
∆[Cl ]k
+∆[Cl]keCl +∆[HCl]keHCl −(k [Cl]+k
)
(11)
2
eCl2
13
eMeCl
ꢂ
•
−
k [R Cl][Cl ] /[R] = k [Cl ] .
7
2
4
2
The plot of this combined flow balance change and chlorinated product forma-
tion kinetics is presented in Fig. 6. Due to the number of rate differences, the
scatter is relatively large, but the rate constant k , given by the slope, agrees
4
well with the value found from Eq. (6).

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
299
Discussion
In spite of a number of small scale side reactions in the Cl/C H /Cl three
2
6
2
component system, the kinetics of C H +Cl reaction, the main object of the
2
5
2
present study can be well established by recording the steady state C H Cl
2
5
formation under different kinetic conditions. This product formation actu-
ally involves reaction 4 and 5 only. The measured rate constant value is
smaller than any value reported previously. It is four times less than the
Goldfinger’s estimate [9], or the value calculated from the C H Cl side-product
2
5
formation kinetics of methane photochlorination [7]. Relative rate measure-
−
12
3
ments report [11, 12] k = (7.8−8.8)·10 cm /(molecule-s), where the scat-
4
ter overlap the differences between the two values, or k = (1.6± 0.25)·
4
−11
3
10
cm /(molecule-s) [15b] when the high pressure limit rate constant of the
reference reaction C H + O is doubled. This latter high value is in agree-
2
5
2
−
11
3
ment with k = (2.1± 0.5)·10 cm /(molecule-s) derived from the real-
4
time measurements of the C H radical consumption rate [8]. The tempera-
2
5
ture dependence measured between 295–498 K has shown a small negative
(
−0.31± 0.12 kcal/mol) activation energy [8]. For unknown reasons, this ac-
tivation parameter is referred to as −0.24 ± 0.72 kcal/mol later on by the
authors [28]. The negative activation energy phenomenon is than interpreted by
the authors [8] as a two-step transition state (TS) mechanism: a loose polar TS1
formed first followed by a tight (or cyclic) TS of lower potential. The polar
2
character of the TS complex leads to an unusually high A-factor for all R+Cl
2
type reactions, where R stands for hydrocarbon radicals. These high A-factors
are proportional to ionization potentials of R (see Fig. 6 of [8b]). Consequently,
the reported A-factor for reaction 4 is 2.5 times higher than for CH + Cl re-
3
2
action [8]. Such a complicated TS mechanism does not withstand analysis [16]
of atom transfer reactions proceeding over a potential well. The idea of a po-
larized TS was only suggested for the reaction CH +BrCl to account for the
3
faster Br than Cl atom transfer which is in contrast to the exothermicities of the
two possible reaction channels [29]. The 3 electron TS for this reaction puts ex-
cess electron densities on Cl which is more favorable than putting it on Br and
can account for the faster Br abstraction.
A reliable empirical approximation of the experimental A-factor can be
◦‡
achieved by estimating the entropy of activation ∆S from the entropy change
of an appropriate model reacton and correcting it with partial entropy contribu-
tions for mass changes and changes in the degrees of freedom [30].
ꢃ
◦‡
= (S model− S◦ − S◦Cl)+
◦
◦
∆
S
∆S (corrections) ,
RCl
where
ꢃ ∆
◦
◦
◦
◦
S (corrections) = ∆S (transl.)+∆S (rot.)+∆S (vibr.)
◦
◦
+
∆S (electr.)+∆S (sym.).

3
00
O. Dobis and S. W. Benson
Each term on the right sides of these equations can be calculated using known
thermochemical functions [30]. The details of such calculation using two dif-
ferent models are given in Table 3. One of the models is a Cl atom insertion for
‡
modeling the reverse process of reaction 4 (RCl+Cl → [R•Cl•Cl] ), then cor-
◦
recting for the standard entropy change ∆S . The other one is an isodesmic
298
change with sulfide substitution. Both models give about the same activation
entropy change. The usual uncertainty of such thermochemical model estima-
tions are about 1 e.u.
Correcting the overall entropy changes in Table 3 from pressure to concen-
−12
3
tration unit, A = 1.3·10 cm /(molecule-s) is obtained. This value is about
4

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
301
1
0 times less than the reported experimental A -factor [8] derived from ethyl
4
radical consumption kinetics and 19 times less than that obtained from the very
minor C H Cl formation in methane chlorination [7].
2
5
Combination of the calculated A -factor with the measured k rate con-
4
4
stant shows that reaction 4 has a small, but positive activation energy of
.13 kcal/mol. This indicates that reaction 4 is a normal atom transfer process
0
involving a single TS.
k is 35% higher than the reported value [8] derived from CH radi-
4
3
cal consumption kinetics, but it overlaps within the scatters, and is about
twice as high as the result deduced from decay time measurements [31]
*
of the vibrationally excited CH Cl product formation. Studies of the pho-
3
tochlorination of methane [4, 6, 7, 24] report lower k11 values by an order
of magnitude for this chain propagation step, where temperature depen-
dency leads to higher activation energy (2.2 kcal/mol) and higher A-factor
of A11 ∼ 1.5·10− cm /(molecule-s) than the isolated reaction 11 measure-
11
3
ments [8].
A quick empirical estimation of the activation entropy change of re-
action 11 – using similar calculations as for Table 3 – is summarized in
‡
Table 4. Both models give the same ∆S which corresponds to A11
5
=
p
−12
3
.0·10 cm /(molecule-s). This value is the same as that deduced from the
measurements of CH consumption kinetics [8], but 3 times lower than the
3
above A derived from the photochlorination of methane. It is about four times
11
higher than A which reflects the 3 e.u. smaller negative entropy change [16] of
4
reaction 11 over that of reaction 4.
Combination of the measured k11 rate constant with the calculated A11-
factor shows that reaction 11 has a small activation energy of 0.23 kcal/mol,
one tenth of the value derived form methane photochlorination studies [7], but
it is in fair agreement with the reported low activation energy derived from the
methyl radical consumption kinetics [8].
Conclusions
The reaction of C H +Cl (reaction 4) was investigated in the Cl/C H /Cl
2
5
2
2
6
2
three component mixture using an overall measurement of reactants and prod-
ucts under steady state flow conditions in the VLPR system. Both the Cl
and Cl as well as the ethane consumptions give excellent mass balances
2
with product formations as shown in Figs. 3 and 4. The rate constant de-
rived from the C H Cl product formation kinetics is found to be k = (1.05±
2
5
4
−12
3
0
.05)·10 cm /(molecule-s) at room temperature. This value is smaller than
k values reported earlier. Two independent estimates of the A factor give
4
−12
3
A = 1.3·10 cm /(molecule-s). Combining it with the measured rate con-
4
stant k , a small positive activation energy of E = 0.13 kcal/mol is obtained
4
4
in contrast with the earlier reported [8] negative activation energy.

3
02
O. Dobis and S. W. Benson
Analysis of the overall product formation reveals a number of side reac-
tions initiated by H atom contamination in the system, all of small extent.
One of them is the CH Cl formation arising from the CH +Cl reaction 11.
3
3
2
Since the CH Cl product is measured, k can be determined from this prod-
3
11
−12
3
uct formation kinetics as k = (3.4± 0.3)·10 cm /(molecule-s). Within the
11
scatters, this value is in agreement with a recently reported [8] value, but is
higher than the values from earlier measurements [3, 7, 31]. Estimation of the
−12
3
A factor gives A = 5.0·10 cm /(molecule-s) in good agreement with re-
11
ported direct result [8] from the temperature dependency of k . It is about 4
11
times larger than A which fits well with the 3 e.u. overall difference in entropy
4
changes [16] of reactions 4 and 11.

Detailed Kinetic Investigation of the C
2
H
5
+ Cl
2
Reaction . . .
303
Of great interest is the observation that no C or C or dichloro products are
3
4
formed in these reactions. At much higher pressures this would not be the case.
Acknowledgement
Acknowledgement is made to the donors of the Petroleum Research Fund ad-
ministered by the American Chemical Society, for the support of this research.
We are also indebted to Professor Irving S. Reed of the Electrical Engineering
Department at USC for a grant in support of the present work.
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